The Red Devils' 2-1 loss to Swansea in the FA Cup was their fifth home defeat of the season, while they have slumped to seventh place in the Premier League table – 11 points behind leaders Arsenal.
But Mourinho feels the pressure Moyes is supposedly under is a fabrication of the media, and is convinced the club will support the man they picked to succeed Sir Alex Ferguson last summer.
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“The most important thing in all of this is not the pressure that comes from the outside, it’s the reality of the inside. My feeling, which is based on years of communicating with Sir Alex and some inside information, is Man United are not happy, but they are calm. They trust David. David trusts them.
“Are the players blaming the manager and thinking ‘I am safe’? No. The players don’t feel that. They feel all together on this. The manager is calm and they are thinking this is our manager for the next two-three-four-five years. So they’re all together and are going to rebuild again a big team.
“The bad results will finish. They will get back on track, probably too late to win the league because they’re too many points behind the leader.
“The gap is difficult to recover but David has a fantastic job. He’s in probably unique conditions to be stable and to do his work well and achieve success sooner rather than later.”
Chelsea host Manchester United at Stamford Bridge on Sunday, with the Blues looking to keep pace with the leaders while Moyes' men eye a top-four berth.